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This should interest all those researching ancient measures - the author connects up the old Saxon foot with other measures in a fascinating study.You can download the article in pdf form from the DSGB site.Rollrights

About 700 years ago, King Edward I decided that there should be onestandard of length for the entire country. He was the first English king to setout tables of length and area measurement. Under this system, the new footwas a little longer than the Roman pes and a little shorter than the Saxon fot.

This led to a problem. Land was measured in Saxon units. One of these wasa rod, equal to 15 Saxon feet. The king did not dare change landmeasurements, so he made the rod equal to 16.5 new feet, or the same as15 Saxon feet. This meant that farmers’ fields would be the size they hadalways been.

So why didn't he just standardize on the Saxon foot? Seems it would have made things easier.

So why didn't he just standardize on the Saxon foot? Seems it would have made things easier.

I imagine somebody will give us chapter and verse, but I imagine there were conflicting requirements. The Roman influence probably still held a lot of support with its 12 inches to the foot, the palm of 3 inches, the hand of four inches, the span of 9 inches and the digit of 3/4 inch (16 digits to the foot). The new foot retained these relationships whereas the Saxon foot would require more changes to make it the standard.

Don't forget that it was the Romans who popularized the division of units into twelfths, simply because of the greater divisibility versus tenths. This was perpetuated throughout Europe, with national versions of lengths equivalent to the foot that differed marginally from country to country and even area to area, but with the same subdivisions. This was also enshrined in later monetary systems implemented initially by Pippin and then his son Charlemagne, resulting in the livre of 20 sous and the sou of 12 denier. Have a look at my avatar, the Roman pocket abacus. The second column from the right is for unciae, so there are five beads in the lower slot and the bead in the top slot has a value of 6 uncia allowing for counting from 1 to 11 uncia. The first column was for fractions of an uncia.

Anyway, the change of the rod probably involved far less disruption than using the Saxon foot as the standard.

Anybody who wishes to add or correct me on this, please do, I would prefer the correct detail.

[QUOTE=Dan,Jul 7 2009, 03:27 AM]Have a look at my avatar, the Roman pocket abacus. The second column from the right is for unciae, so there are five beads in the lower slot and the bead in the top slot has a value of 6 uncia allowing for counting from 1 to 11 uncia. The first column was for fractions of an uncia.

That's pretty slick, Ruthe. I think I'm going to have to build such an abacus soon. It's not as powerful as a slide rule, of course, but I rarely need the extensive capabilities of such, and it would require a lot less precision to build.

(I have calculators, of course. I've just always been fascinated by mechanical, non-electrical devices.)

(I have calculators, of course. I've just always been fascinated by mechanical, non-electrical devices.)

The picture of the Roman abacus is that of a reproduction made from an image found on a Roman column frieze. Columns 3 to 9 are an example of a bi-quinary abacus where the beads in the lower slots counted as one of that column's value while the bead in the top slot had a value of 5. The symbols in the gap between the upper and lower slots indicate that the value of each column was 10 times that of the column to the right, starting with ones in column 3 and going up to millions in the last column.

This demonstrates that although the Romans had no written form for zero, they did recognize the significance of a zero value in each column represented by no beads moved to the counted position which I assume was the centre gap between the lower and upped slots. This then shows the Romans used a decimally based, place value system for performing calculations.

A further characteristic that becomes evident, is that Roman written values could be easily transferred to the abacus and likewise the result of calculations transferred back to their written notation. As examples, a value of 5 (Roman V) was just the single bead in the top slot of column 3, and values of 50, 500 etc (Roman L, D) the upper bead in columns 4,5 and so on.

This abacus is said to have been in use around 50AD and was approximately 120 mm x 80 mm or 5" x 3 1/8", making it marginally wider but no longer than my Sharp calculator. In other words, the world's first pocket calculator!!!!

Jim,How ancient is ancient? If we are talking before 1 AD only some cultures were decimal. Positional notation was not common among societies, especially less than the radix point. If the "ancients" converted the cube root of 2 to any ratio, perhaps it was 5/4. The Romans may have expressed it as 1 and 3 uncić, and going back further the Babylonians would have a shortened sexagesimal form of 1:15,35,42,56,48,23,53,42,43,42,47,05,40... Again, maybe only 1:15, since they were fond of regular numbers, and 1,15 is regular. If the cube root of two was known, it would seem 1.26 may be too "decimal", and folks would've used 5/4 sooner than (5/4 + 1/100).

I think the Indus Valley could be considered ancient and so when I read this reference I considered it important. I imagine the sample rule mentioned is available to study.

It is remarkable how near this early decimal system of Germany and Britain is the double of the modern decimal metric system. Had it not been unhappily driven out by the 12 inch foot, we should need but small change to place our measures in accord with the metre.’

From “The Roots of Ancient India”, The Archaeology of Early Indian Civilisation, second edition, revised, by Walter Fairservis Jr. (page 291).;

‘… linear measurement was apparently well standardised. Mackay by good fortune found a piece of shell marked in regular fashion and quite clearly intended as a rule. Nine divisions remain, and from circular markings at two placed five units apart it would appear that a decimal system was in vogue. Each division is approx 0.264 inches wide, or a five-unit total of 1.32 inches. Thus a foot in the decimal system would be 13.2 inches, which fit into a widespread system of the ancient world. Similarly Vats and Wheeler provided evidence that a cubit was also used. Thus both the smaller and larger units of measurement were used in building and presumably to lay out fields.’

This is mentioned in other texts, the implication being that the circumference of the Earth was known in ancient times; but the correspondence to the metre suggests also that the circumference was divided as today - first into quarters, and then decimally into metres.Most measures in the ancient world reflect the fact that the circumference was divided sexagesimally (by sixties).

I hope some of you find this interesting. It was for me but not being into math I have often wondered if anyone would be interested.

How to double the volume of a cube by construction by changing its shape.

I am sure you guys would be pretty good at this but here is one way which I have found and published in a local magazine many years ago.

Turn a cube into a pyramid and in the process double its volume exactly.

I was looking at the three pyramids of Giza and noticed that the third pyramid Mycernius was approximatly 1/10th the volume of the Great pyramid. I had used the measurements give by I E S Edwards who wrote the Pyramids of Egypt.

Edwards gave the base length of the third pyramid as 356.5 feet which differed quite significently to Flinders Petries measure. Never the less I persisted and decided to use a combination of the numbers 3456 so made 356.4 Imperial feet as the base of the third pyramid.

I had already noted that this number times 3 equaled the diagonal of the Great Pyramid.

I thought to myself 'What if the architect of the pyramid had intended building a cube on the base and not a pyramid so just for the exercise I decide to treat the base of the third pyramid as the base of a cube.

The volume of such a gigantic cube 356.4 cubed = 45,270,270.14 cubic imperial feet and by doubling this 90,540,540.29 comes close but does not exactly equal the volume of the Great pyramid.

As I said earlier I had noticed the base of the third pyramid was 1/3rd that of the diagonal of the Great pyramid.

356.4 x 3 = 1069.3 imperial feet for the diagonal of the Great Pyramid. This renders a base of 756.0385704 and 756 feet is commonly used to denote the base of the Great pyramid.

And so I started from there and wondered how to find a height that would deliver a volume twice that of the imagined cube.

By trial and error I dived the base of the third pyramid by 3 ie 356.4 divided by 3 = 118.8 and multiplied by 4 = 475.2 imperial feet, and so this would become the height of the imagined pyramid.

This did not equal the actual height of the Great Pyramid but would have reached the base of the capstone, which Agathachides said was 4 cubits in height.

In any case this method doubles the cube exactly by changing its shape.

Hi Wendy I corresponded with R D Connor for a time and I would like to quote a portion of one of his letters.

Connor

9th January 2002

'I quote from Philip Grierson's English Linear Meausres, University of Reading 1972, p6.

[Peoples are supposed to have been] addicted to borrowing the weights and measures of other people, however remote from themselves in time and place. Thus Flinders Petrie - I choose deliberately a great name, that of one of the creators of modern archaeology - is ready to assure us that the Parthenon and Stonehenge were alike constructed to a foot of 11.68 or 11.69 inches, derived from the Egyptian remen of 19.161 inches while the builders of neighbouring Erechtheum preferred to employ the North Syrian or Phoenician foot of 11.09 inches.

................

Such beliefs and inferences belong, in my opinion, to the realm of fantasy.'

Connor was not impressed with suggestions that measures can be found by reference to ancient monuments such as the Great Pyramid.

I quote Connor ' This I do not subscribe to but at the same time I must say that my forthcoming book on the Weights and Measures of Scotland show a great inter - dependence of French, English and Scottish metrologies than I had expected.'

I had put to him that the Mile is constant

48005000 5280 7200

all equal 6336 inches and are a part of the very same system. The foot equals...

The Indus Valley or Saxon or as you have said the Rollrigh 13.2 inchesThe Roman 12.672 inchesImperial 12 inches7200 is in fact a span of 8.8 inches

The common root could be the imperial foot, If it represents the number 100 so 0.12 of an inch represents one then we can divide the variosus feet you have identified by 0.12 to see what numbers are represented,

congratulations on having your paper accepted by the European Association of Archaeologists very recently. August/September 2017 meeting at Maastricht in Holland.

Since you wrote it in 2006 it is testament to your preseverance that you have promoted it for so long and finally have been accepted by the Scientific Branch of the Association. This should send out notice to anyone interested in these units of ancient measure.( noting 10x11x12) Jim's unit is accepted now as extremely ancient and 4 x 1320 = 5280.

Have you had any feedback in Australia as a result? It seems to be good times since Plimpton 322 has been decoded and the paper is excellent, a huge breakthrough in our understanding of ancient mathematics and its unusual complexity.

As far as i am aware you are the only researcher who has recorded the area of the stone circles as containing astronomical information. It is a unique position to be in and i hope the dozenal demigods and disciples take note of this. Pi as 22/7 is the translator but also fibonacci pi that you are promoting.

Also the Greek foot as 12.6 inches and this ties in exactly with my findings in respect of the Greek foot.

If the imperial foot is a metric unit representing 100 units then it is 8.33333r units to the inch.

12.6 x 8.333r = 105. this is the ratio of the Greek/Roman foot to Thom's megalithic foot as 102/105 = 0.971428571

102 / 8.3333r being 12.24 x 8/3 = 32.64.

The unit is identified in Anne Macaulay's book 'Megalithic Measures and Rhythms'

In my book 'proving the megalithic yard' this 100 unit length of the foot is explored as above and is part of the proof.

i have not got involved with the Sarsen circle but 0.971428571 x 100 is a suggested circumference by several metrologists.Also it has been suggested it is one day so one week is 97.1428571 x 7 = 680 exactly 10 of Thom's megalithic rods.

Your unit 1320 x 34/33 = 1360 half of 100 megalithic yards.

Also this fibonacci version of pi seems to work with the actual circumferences as follows

'The Origin of Numerical Systems and the Manipulation of Pi and Other Mathematical Constants.

Our ancestors appear to have manipulated numerical systems based on their understanding of natural numbers. The imperial is a naturally occurring system of number based on the doubling of base two and multiplying by the sequential primes from three to eleven and removing base 7 through the design of Pi used within the system. Pi is used as 1760/560 or initially as 22/7.

The system Thom discovered is designed exactly the same way but the primes are taken to base 17, removing base 13 through the design of Pi. Pi is used as 1632/520 or initially as 40.8/13. '

Having the paper 'From the Rollrights to Stonehenge' accepted by the Association of European Archaeologists is a huge step forward for the 21st century metrologists investigating the design of the ancient stone circles.

The Saxon foot 1.1 English feet is the unit of translation to produce astronomical information in the perimeters and diameters and possibly more importantly the areas of the circles and ellipses. This is a stepping off point into the past that has been considered and accepted and can be used as a focus to drive futher investigations.

There is a problem at Stonehenge in that many investigations pluck the diameter and circumference seemingly out of thin air.

It is important to set a standard for the Saxon foot to be used against, when investigating Stonehenge, and it involves sorting out the wheat from the chaff, in respect of completed and recorded Stonehenge investigations.

Professor Mike Parker Pearson has co authored a paper that identifies the diameter of the first phase of Stonehenge the Aubrey circle as 285.60 imperial feet. He is the current person in charge of all work at Stonehenge so this can be considered reasonably reliable evidence. This diameter is also confirmed to the findings of Professor Alexander Thom in the 1960's amd 70's. He confirmed that the circumference was required to be in whole numbers often expressed in units of 2.5 of the base unit.

Thom also confirmed, based on an investigation he supervised but did not carry out, that the diameter of the postholes from centre to centre was 283.60 feet giving the radius of the postholes as 1 imperial foot exactly. It is important to realise that Thom was given 'carte blanche' to investigate Stonehenge, this is how highly his work was rated at the time.

So the baseline for further investigation is set. Use the Saxon foot against a diameter of 285.60 English feet and use pi as 22/7 remembering that there is a possibility that units of one English foot are held within the design.

This starting point is based on well researched and recorded findings and is well know to all archaeologists but not necessarily clarified until now.

Applying the use of the Saxon foot to the diameter produces a strange decimal number

285.6 / 1.1 = 259.6363636r.

It is important at this point, to introduce one of the 'rules' for further investigation.

Explain your decimals. This is possibly the worst way to engage a reader with a theory on Stonehenge. They simply did not do decimals. They probably used fractional maths as 22/7 indicates. Fractions certainly offer a better understanding of the reasoning applied to the design of the circles.

So 259.63636363636r --- what is it as a fraction because these recurring decimals can always be expressed in fractions?

But the starting point is also decimalised as 285.60.

This can be overcome by making the English foot represent 100 units so 28560 is the starting point.

The diameter is then expressed as 28560 / 110 in Saxon feet.

So now it can be multiplied by the Pi approximation of 22/7.

28560/110 x 22/7 = 628320/770 = 816.

This is the base unit in the system discovered by Thom. So the Aubrey Circle is 816 Saxon feet. Dividing by 2.5 or 5/2 gives 3264/10 and this is an expession in Thom's megalithic yards.

In terms of astronomical units the Nodal cycle of the Moon is 6800 days and this divides by 2.72 the unit Thom has been repeatedly challenged against and has now been cast aside by the whole of the archaeology profession.

6800 / (272/100) = 2500.

Thom never made this link in his work but it is there at Stonehenge without question using bona fide evidence that is reliable.

This starting point was established in my first book but without the Saxon foot, and what an enormous difference it makes!!

The theme throught the book is ---without Thom's work ---we have no starting point for investigation.

The starting point is now redefined as the circumference of the Aubrey circle is 816 Saxon feet using a unit accepted as ancient by the European Association of Archaelogists.

The dreaded decimal places disappear and the explanation becomes very simple using the imperial base 12 system.

So the acceptance of Wakefield's paper signifies a turning point and a reference point that needed to be established.

My first book is sold out except for a few copies in my local bookstore at Scarthin Books, Cromford, Derbyshire. A second print run is not being considered.

The book lays out a methodology for the investigation of the Stonehenge first phase the Aubrey circle. The Sarsens came much later. When written the link between the imperial and Thom's system had not been established despite countless hours of computer modelling. It is ironic that when it was discovered it was a simple 33/34 relationship.